15.88 (2002)

Let $\mathfrak{A}$ and $\mathfrak{N}_c$ denote the varieties of abelian groups and nilpotent groups of class $\leqslant c$, respectively. Let $F_r = F_r(\mathfrak{A}\mathfrak{N}_c)$ be a free group of rank $r$ in $\mathfrak{A}\mathfrak{N}_c$. An element of $F_r$ is called primitive if it can be included in a basis of $F_r$. Does there exist an algorithm recognizing primitive elements in $F_r$?